Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in JAVA):

Solution:
import java.math.BigDecimal;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] a = new long[n];
        long cd, ab;
        double result;

        for(int i = 0; i < n; i++) {
            a[i] = sc.nextLong();
        }

        Arrays.sort(a);
        result = (double)(a[n - 1] + a[n - 2]) / (double)(a[1] - a[0]);
        for(int i = 1; i < n - 1; i++) {
            if(i + 1 == n - 1) {
                cd = a[n - 1] - a[n - 2];
                ab = a[n - 3] + a[n - 4];
            } else if(i + 1 == n - 2) {
                cd = a[n - 2] - a[n - 3];
                ab = a[n - 1] + a[n - 4];
            } else {
                cd = a[i + 1] - a[i];
                ab = a[n - 1] + a[n - 2];
            }
            result = Math.max(result, (double)ab / (double)cd);
        }
        System.out.printf("%.6f\n", result);
        }
}